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Show that f(x)={(xsinfrac{1}{x},xne0),(0,x=0):} is not differentiable x=0

Answer»

Solution :`L.H.D.=lim_(hto0)(f(-h)-f(0))/(-h)`
`=lim_(hto0)((-h)sin(-1/h)-0)/(-h)=lim_(hto0)(-sinfrac{1}{h})`
which does not EXIST.
SIMILARLY R.H.D. does not exist.
So f(X) is not differentiable at x=0


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